Kronecker Algebra consists of Kronecker Product and Kronecker Sum. This mathematical model can be used to model systems consisting of a number of limited resources and several actors. In particular, it can be used to model railway systems with trains, track sections and their routes. In this paper we show several applications of Kronecker Algebra in the railway domain. We consider deadlock prevention, travel time calculation, and energy analysis. The integration of these three tasks within one single type of Kronecker-based analysis is rather simple and can be carried out very efficiently. Due to the fact that Kronecker Algebra operations can be easily parallelized, our implementation can take full advantages of today's multi-core computer architecture. In addition our implementation shows that adding constrains for connections or overtaking speeds up the calculation. In fact, a harder problem is easier to solve.

Kronecker Algebra; railway systems; deadlock; travel time; energy analysis